This function calculates a variance stabilizing transformation (VST) from the
fitted dispersion-mean relation(s) and then transforms the count data (normalized
by division by the size factors or normalization factors), yielding a matrix
of values which are now approximately homoskedastic (having constant variance along the range
of mean values). The transformation also normalizes with respect to library size.
rlog is less sensitive
to size factors, which can be an issue when size factors vary widely.
These transformations are useful when checking for outliers or as input for
machine learning techniques such as clustering or linear discriminant analysis.
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a DESeqDataSet or matrix of counts
logical, whether to blind the transformation to the experimental design. blind=TRUE should be used for comparing samples in a manner unbiased by prior information on samples, for example to perform sample QA (quality assurance). blind=FALSE should be used for transforming data for downstream analysis, where the full use of the design information should be made. blind=FALSE will skip re-estimation of the dispersion trend, if this has already been calculated. If many of genes have large differences in counts due to the experimental design, it is important to set blind=FALSE for downstream analysis.
in case dispersions have not yet been estimated for
For each sample (i.e., column of
counts(dds)), the full variance function
is calculated from the raw variance (by scaling according to the size factor and adding
the shot noise). We recommend a blind estimation of the variance function, i.e.,
one ignoring conditions. This is performed by default, and can be modified using the
Note that neither rlog transformation nor the VST are used by the
differential expression estimation in
DESeq, which always
occurs on the raw count data, through generalized linear modeling which
incorporates knowledge of the variance-mean dependence. The rlog transformation
and VST are offered as separate functionality which can be used for visualization,
clustering or other machine learning tasks. See the transformation section of the
vignette for more details.
The transformation does not require that one has already estimated size factors and dispersions.
A typical workflow is shown in Section Variance stabilizing transformation in the package vignette.
estimateDispersions was called with:
a closed-form expression for the variance stabilizing
transformation is used on the normalized
count data. The expression can be found in the file ‘vst.pdf’
which is distributed with the vignette.
the reciprocal of the square root of the variance of the normalized counts, as derived
from the dispersion fit, is then numerically
integrated, and the integral (approximated by a spline function) is evaluated for each
count value in the column, yielding a transformed value.
fitType="mean", a VST is applied for Negative Binomial distributed counts, 'k',
with a fixed dispersion, 'a': ( 2 asinh(sqrt(a k)) - log(a) - log(4) )/log(2).
In all cases, the transformation is scaled such that for large counts, it becomes asymptotically (for large values) equal to the logarithm to base 2 of normalized counts.
The variance stabilizing transformation from a previous dataset
can be frozen and reapplied to new samples. See the 'Data quality assessment'
section of the vignette for strategies to see if new samples are
sufficiently similar to previous datasets.
The frozen VST is accomplished by saving the dispersion function
dispersionFunction, assigning this
DESeqDataSet with the new samples, and running
varianceStabilizingTransformation with 'blind' set to FALSE
(see example below).
Then the dispersion function from the previous dataset will be used
to transform the new sample(s).
Limitations: In order to preserve normalization, the same
transformation has to be used for all samples. This results in the
variance stabilizition to be only approximate. The more the size
factors differ, the more residual dependence of the variance on the
mean will be found in the transformed data.
rlog is a
transformation which can perform better in these cases.
As shown in the vignette, the function
from the package vsn can be used to see whether this is a problem.
varianceStabilizingTransformation returns a
DESeqTransform if a
DESeqDataSet was provided,
or returns a a matrix if a count matrix was provided.
Note that for
DESeqTransform output, the matrix of
transformed values is stored in
getVarianceStabilizedData also returns a matrix.
Reference for the variance stabilizing transformation for counts with a dispersion trend:
Simon Anders, Wolfgang Huber: Differential expression analysis for sequence count data. Genome Biology 2010, 11:106. http://dx.doi.org/10.1186/gb-2010-11-10-r106
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